We study numerically the propagation of fluxons along two Josephson transmission lines which are coupled by an inductive element. This structure, for particular choices of the coupling parameters, reveals an interesting variety of nonlinear phenomena. The numerical simulations show good qualitative agreement with analytical calculations regarding the most significant events (reflection and transmission of fluxons). Experimental results obtained from real Josephson devices are also reported and the possible application of these devices is discussed in detail.